Calculating Dependant Probability of Multiple Events

The Problem

-There are 5850 total tickets.
- 8 tickets will be randomly chosen at the same time.
- Once a ticket is chosen, the same ticket number cannot get chosen again.
- I have 290 tickets or 3.57% of the total supply.
- There is a reward structure if you get 3 tickets, 4 tickets, 6 tickets, and 8 tickets you win a prize.
- What is the probability that my 290 tickets get picked 1 time, 2 times, 3 times, 4 times, 5 times, 6 times, 7 times, and all 8 times, and what is the formula to calculate that?

What I have so far

I believe I was able to calculate the probability of getting 1 ticket (290*8/5850 = 28.58%)

I get confused once I need to calculate it happening 2 times and on. Would it be (289*8)/(5850*2) or (289*7)/(5850*2)?
  • Do you mean the following? "There are 5850 tickets, among them 8 are "winning". I have 290 tickets. What is the probability of me having 1, 2, ..., 8 winning tickets?"

  • Yes - if your ticket is chosen then it can be redeemed for a prize thus it would be considered a winning ticket.

  • I accepted but I am unable to understand the formula and I am not gifted in math. What does "!" mean in the equation How did you get 5842? That is 18 minus 5860 which I am not sure where that comes from. Can you help me in more layman terms on how to solve?

  • The ! (factorial) symbol means you have to multiply by all the numbers smaller than that, e.g., 5! = 5*4*3*2*1 = 120. For the other question, 5842 = 5850-8, and you have 5850 tickets total, so that is the number of non-winning tickets.

  • The binomial symbol gives you the way of choosing a subset of a set of a given size. I would recommend giving a look to the Wikipedia page to get an idea of what's going on.


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.